Progression with variable in exponent

Question

what is the solution of this kind of progressions:

$1 + \delta^{T} + \delta^{2T} + \delta^{3T} + \dots $

I have tried hard and look through the website but still I don't know hot to solve the issue of the $T$.

Thanks in advance.

Answer 1

$$1 + \delta^T + \delta^{2T} + \cdots = (\delta^T)^0 + (\delta^T)^1 + (\delta^T)^2 + \cdots = \sum_{k=0}^{\infty} (\delta^T)^k = \frac{1}{1 - \delta^T}$$

(Sum of a geometric series)